Bake hair particle system to textured low-poly mesh
I have a technique which might be unorthodox but very efficient.
The idea is to deform your mesh into its UV map while keeping the hair attached to it, so you can render it into a UV texture :



I've used this technique on one model so far and it worked well.
Here's a part of the result :




Downsides


it doesn't perform well on long or clumped hair
it renders noticeable seams on the islands borders


How to prevent them as much as possible:


Prefer sculpting (combing) your hair manually instead of using the Clump property
use as few UV islands as possible. For that, I strongly recommend avoiding Blender's built-in UV unwrapping (which introduces important distortions) and instead, using the SLIM algorithm. You can use it by either installing the original standalone program (not the best because it requires to triangulate your mesh and split the seam edges) or better, by building the Blender SLIM branch (much easier to play with but might be harder to install depending on your OS). Hopefully this amazing algorithm will get implemented in an official release some day.


Now, to deform your mesh into its UV map, you need the UV Shape add-on (not yet updated for 2.8).
Once you have it enabled :


duplicate your model
put the copy on another layer
select your edge seams (select only one and then click on Select > Select Similar > Seam)
perform an Edge Split
in Object mode, select the UV map you want your mesh to deform into
in the Extended Tools tab of the tool shelf, enable "Use Active
Map"
leave "Rescale Islands" enabled to keep hair density consistent   
click on "Create UV shape". This creates a shapekey. The hair should deform well with the mesh. Personally I did it with a rabbit's fur and it worked perfectly. Tell me in a comment if that didn't go well for you.
select the created shapekey
in Edit mode, top view, pack your islands in a square (in 3D view of course).You can rotate islands but don't rescale anything or the hair density will change.
create an orthographic camera and put it on top view
adjust the orthographic scale so the flattened mesh fits in the frame 
project UVs from view
in UV/Image Editor, ensure the UV map fits the UV square. If not, don't rescale directly in the UV/Image Editor. Instead, zoom or unzoom your ortho camera and reproject UVs.
remove any lighting in your scene and set the World color to white
Render with the orthographic camera
Save the image


Now you can bake this texture on the original UV map :


on the non-original model, create a simple diffuse material with
the rendered image as the color texture
select the non-original model and then the original
bake the diffuse color from selected to active (make sure you have an
image node selected to bake into)


and voilà !

You can even render a hair normal map using a camera normal material :


Although you may want to combine it with the normal map from the hi-res mesh if you have one (I have to add a screenshot on how to combine normal maps with Cycles nodes)